Overlapping structure when beveling (SVG) curve
You can do this quite easy with help from TinyCAD add-on and some modifiers.

Steps:


After importing SVG convert it to a mesh - Alt+C > Mesh from Curve/Meta/Surf/Text.
Enable TinyCAD add-on.
In Edit Mode select two crossing edges and W > TinyCAD > VTX Auto. 


  Important! You should have only two edges. Sometimes a little clean up
  could be needed as in example below. Use X > Dissolve Vertices to do this.



Add Skin and Subdivision (use level as needed) modifiers.
In Edit Mode after selecting all vertices scale them with Ctrl+A and tweak Branch Smoothing in Skin modifier as needed.